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Author Sogge, Christopher D. (Christopher Donald), 1960- author
Title Fourier integrals in classical analysis / Christopher D. Sogge
Imprint Cambridge : Cambridge University Press, 1993
book jacket
Descript 1 online resource (x, 236 pages) : digital, PDF file(s)
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
text file PDF rda
Series Cambridge tracts in mathematics ; 105
Cambridge tracts in mathematics ; 105
Note Title from publisher's bibliographic system (viewed on 05 Oct 2015)
5. L[superscript p] Estimates of Eigenfunctions. 5.1. The Discrete L[superscript 2] Restriction Theorem. 5.2. Estimates for Riesz Means. 5.3. More General Multiplier Theorems -- 6. Fourier Integral Operators. 6.1. Lagrangian Distributions. 6.2. Regularity Properties. 6.3. Spherical Maximal Theorems: Take 1 -- 7. Local Smoothing of Fourier Integral Operators. 7.1. Local Smoothing in Two Dimensions and Variable Coefficient Kakeya Maximal Theorems. 7.2. Local Smoothing in Higher Dimensions. 7.3. Spherical Maximal Theorems Revisited -- Appendix: Lagrangian Subspaces of T*R[superscript n]
Fourier Integrals in Classical Analysis is an advanced monograph concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. Using microlocal analysis, the author, in particular, studies problems involving maximal functions and Riesz means using the so-called half-wave operator. This self-contained book starts with a rapid review of important topics in Fourier analysis. The author then presents the necessary tools from microlocal analysis, and goes on to give a proof of the sharp Weyl formula which he then modifies to give sharp estimates for the size of eigenfunctions on compact manifolds. Finally, at the end, the tools that have been developed are used to study the regularity properties of Fourier integral operators, culminating in the proof of local smoothing estimates and their applications to singular maximal theorems in two and more dimensions
Subject Fourier series
Fourier integral operators
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